Antimagic labeling of linear forests

A graph with q edges is called antimagic if its edges can be labeled with 1, 2, ..., q such that the sums of the labels of the edges incident to each vertex are distinct. A linear forest is the union of disjoint paths of orders greater than one. A P-k-free linear forest is a linear forest without any path P-k as its components. It is shown that P-2, P-3, P-4-free linear forests are antimagic. This study improves the result and shows that P-2, P-3-free linear forests are antimagic.